Grade 7: Proportional Relationships

Objective

Students will identify unit rates and constants of proportionality in tables, and determine whether a relationship is proportional by testing for equivalent ratios. Students will practice connecting ratios to unit rates as a foundation for solving proportional relationship problems.

Materials

• "Grade 7: Proportional Relationships" resource (printed copies of 4.1c Class Activity: Model and Understand Unit Rates and 4.1d Class Activity: Finding Unit Rates)
• Pencils
• Whiteboard or chart paper (optional, for reviewing answers as a class)

Warm-up (~5 min)

Write this on the board for students to answer independently:

• "A ratio can be written in three ways. Name them." (Answer: as a fraction, using a colon, or using words — from resource vocabulary/prior knowledge notes.)
• "What is the difference between a part-to-part ratio and a part-to-whole ratio?"

Have 2–3 students share their answers aloud. Do not spend time correcting in depth — this is just to activate prior knowledge from 6th grade ratio work, as noted in the resource's "Prior Knowledge" section.

Main Activity (~25 min)

1. Distribute copies of 4.1c Class Activity: Model and Understand Unit Rates.
2. Explain the goal (write on board): "Today we are modeling and understanding unit rates — a unit rate compares a quantity to 1 unit of another quantity."
3. Have students work through the 4.1c Class Activity problems individually or in pairs for about 12 minutes.
4. Circulate the room. If students get stuck, redirect them to re-read the problem and identify what quantity is being compared "per 1" of another quantity — this is the core skill of this activity per the resource.
5. After 12 minutes, transition to 4.1d Class Activity: Finding Unit Rates. Distribute copies.
6. Have students work individually or in pairs for the remaining ~13 minutes, applying the same unit rate thinking to find unit rates directly.
7. If students finish early, have them check their work with a partner and discuss any differences in their answers.

(Note: If 4.1c or 4.1d activity sheets are not available/printed, use 4.1a Class Activity: Equivalent Ratios, Fractions, and Percents as a review-based substitute — it covers the same 6th grade ratio foundation referenced in this chapter.)

Wrap-up / Exit Ticket (~10 min)

Have students answer the following on a half-sheet of paper (based on today's work):

1. In your own words, what is a unit rate?
2. Pick one problem from today's activity (4.1c or 4.1d) and write the unit rate you found, showing your work.
3. Explain what a ratio is and give one way to write it (fraction, colon, or words).

Collect the exit tickets as students leave, or have them place them in a designated bin.

If Time Remains

Have students turn to a partner and create their own real-world example of a unit rate (e.g., comparing a quantity to "1" of something), similar to the style of problems in 4.1c/4.1d. Ask a few pairs to share their example with the class.